Integral symbol

The integral symbol.

Not to be confused with Long s or Esh (letter).

The ∫ symbol $\int$ is used to denote the integral in mathematics. The notation was introduced by the German mathematician Gottfried Wilhelm von Leibniz towards the end of the 17th century. The symbol was based on the ſ (long s) character, and was chosen because Leibniz thought of the integral as an infinite sum of infinitesimal summands. See long s for more details on the history of ſ.

The ∫ symbol is U+222B in Unicode and \int in LaTeX. In HTML, it is written as ∫ (hexadecimal), ∫ (decimal) and ∫ (named entity).

The original IBM PC code page 437 character set included a couple of characters ⌠ and ⌡ (codes 244 and 245, respectively) to build the integral symbol. These were deprecated in subsequent MS-DOS code pages, but they still remain in Unicode (U+2320 and U+2321, respectively) for compatibility.

The ∫ symbol is very similar to, but not to be confused with, the (ʃ) symbol (called esh).

Related symbols are ∬ (double integral, U+222C), ∭ (triple integral, U+222D), ∮ (contour integral, U+222E), ∯ (closed surface integral, U+222F), and ∰ (closed volume integral, U+2230).

Typography in other languages

Regional variations (English, German, Russian) of the integral symbol.

In other languages, the shape of the integral symbol differs slightly from the shape commonly seen in English-language textbooks. While the English integral symbol leans to the right, the German symbol (used throughout Central Europe) is upright, and the Russian variant leans to the left.

Another difference is in the placement of limits for definite integrals. Generally, in English-language books, limits go to the right of the integral symbol: $\int _{0}^{T}f(t)\;dt$

By contrast, in German and Russian texts, limits for definite integrals are placed above and below the integral symbol and as a result the notation requires larger line spacing: $\int \limits _{0}^{T}f(t)\;\mathrm {d} t$

References

• Stewart, James (2003). "Integrals". Single Variable Calculus: Early Transcendentals (5th edition ed.). Belmont, CA: Brooks/Cole. p. 381. ISBN 0-534-39330-6. {{cite book}}: |access-date= requires |url= (help); |edition= has extra text (help)
• Zaitcev, V.; Janishewsky, A.; Berdnikov, A. (1999), "Russian Typographical Traditions in Mathematical Literature" (PDF), EuroTeX'99 Proceedings {{citation}}: Missing or empty |title= (help)

External links

• Fileformat.info